Police are hunting a man who they say stabbed his de facto partner to death outside shops at Sunshine in Melbourne's west.

Police say the attacker, a 38-year-old Sunshine North man, used what is believed to be a fishing knife to stab the 33-year-old woman several times in the chest on the corner of Hampshire and Devonshire roads about 12:30pm (AEST) on Wednesday.

Detective Senior Sergeant Stuart Bailey says the man had been the de facto partner of his victim for 18 years and the pair had been in court earlier that day over a dispute.

"Our victim left court and attended a women's refuge. After leaving that women's refuge she attended her solicitor's office in Hampshire [Road].

"She left, walked out of that, and three minutes later was attacked by her de facto partner."

Lieu, who works in a nearby shop, says she saw a man stabbing the woman in her stomach and neck.

"I heard the woman yelling, calling for help and I just ran out to have a look and I saw a man with her," she said.

She says passers-by chased after the attacker but were unable to stop him driving away.

"The man with a knife, he ran into the car and two men ran after him to catch him," Lieu said.

"They ran until they caught the car; he locked the car and he [got] away."

His car was found abandoned in nearby Anderson Street.

Detective Bailey says the attacker has a history of domestic violence but would not go into detail about the nature of the court dispute.

"There is an intervention order that is a court issued intervention order but I can't go into whether this case is related to that," he said.

"There has been domestic violence issues between the two before.

"It's an atrocious crime. We have some kind of dispute that occurred at court... and we were hoping the dispute could have resolved by the court itself."

Police say the pair have four children together and one of them may have witnessed the attack.

The man is about 175 centimetres tall and has a slim build.

He has dark hair and a goatee and was last seen wearing a black hooded jumper, black jeans and blue runners.